Advertisements
Advertisements
प्रश्न
Ten different letters of alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have atleast one letter repeated is ______.
पर्याय
69760
30240
99748
99784
उत्तर
Ten different letters of alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have atleast one letter repeated is 69760.
Explanation:
Number of 5 letters words (with the condition that a letter can be repeated) = 105 .
Again number of words using 5 different letters is 10P5 .
Therefore, required number of letters
= Total number of words – Total number of words in which no letter is repeated
= 105 – 10P5
= 69760.
APPEARS IN
संबंधित प्रश्न
How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?
In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?
Find x in each of the following:
Which of the following are true:
(2 × 3)! = 2! × 3!
In how many ways can 7 letters be posted in 4 letter boxes?
Write the number of all possible words that can be formed using the letters of the word 'MATHEMATICS'.
If in a group of n distinct objects, the number of arrangements of 4 objects is 12 times the number of arrangements of 2 objects, then the number of objects is
The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive, is
The number of ways in which the letters of the word ARTICLE can be arranged so that even places are always occupied by consonants is
Find x if `1/(6!) + 1/(7!) = x/(8!)`
How many five digits telephone numbers can be constructed using the digits 0 to 9 If each number starts with 67 with no digit appears more than once?
If nP4 = 12(nP2), find n.
Find the number of arrangements that can be made out of the letters of the word “ASSASSINATION”.
- In how many ways can 8 identical beads be strung on a necklace?
- In how many ways can 8 boys form a ring?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if question number n has n + 1 choices?
If the letters of the word GARDEN are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, then find the ranks of the words
GARDEN
If the letters of the word GARDEN are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, then find the ranks of the words
DANGER
Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?
In how many ways can 5 children be arranged in a line such that two particular children of them are always together
In how many ways can 5 children be arranged in a line such that two particular children of them are never together.
There are 10 persons named P1, P2, P3, ... P10. Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.
The total number of 9 digit numbers which have all different digits is ______.
The number of permutations of n different objects, taken r at a line, when repetitions are allowed, is ______.
The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.
In the permutations of n things, r taken together, the number of permutations in which m particular things occur together is `""^(n - m)"P"_(r - m) xx ""^r"P"_m`.
How many words (with or without dictionary meaning) can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
| C1 | C2 |
| (a) 4 letters are used at a time | (i) 720 |
| (b) All letters are used at a time | (ii) 240 |
| (c) All letters are used but the first is a vowel | (iii) 360 |
Let b1, b2, b3, b4 be a 4-element permutation with bi ∈ {1, 2, 3, .......,100} for 1 ≤ i ≤ 4 and bi ≠ bj for i ≠ j, such that either b1, b2, b3 are consecutive integers or b2, b3, b4 are consecutive integers. Then the number of such permutations b1, b2, b3, b4 is equal to ______.
8-digit numbers are formed using the digits 1, 1, 2, 2, 2, 3, 4, 4. The number of such numbers in which the odd digits do no occupy odd places is ______.
